1. Field of the Invention
The present invention relates to a position control system for use with a machine tool or the like, and more particularly to a position control system having a position control loop with improved quick response capability as well as stability maintained at a desired level.
2. Description of Background Art
FIG. 1 of the accompanying drawings illustrates a software-implemented servo system which has widely been used heretofore as a position control system for use with a machine tool or the like.
The illustrated position control system comprises a position control loop having a relatively low gain .omega..sub.0 with respect to a position command and a speed control loop having a relatively high gain .omega..sub.c with respect to the position command.
Because the speed control loop of this position control system has a high gain .omega..sub.c, the position control system is less susceptible to disturbances and parameter changes. Furthermore, since the position control loop has a low gain .omega..sub.c, the mechanical system is not subject to excessive shock (acceleration), and hence no special care is required in preparing a machining program for an NC machine tool or the like.
However, the position control system of the type described above has the following problems:
Inasmuch as the maximum value of the gain .omega..sub.0 of the position control loop is limited by the allowable maximum acceleration and maximum speed of the mechanical system, the response time cannot be increased beyond the maximum values. Since the control positional accuracy is limited by the maximum value of the gain .omega..sub.0 of the positional control loop, the positional accuracy cannot be increased beyond the maximum gain.
The above problems are of great importance in modern positional control which requires high accuracy. The positional control loop of the conventional positional control system shown in FIG. 1 has a characteristic G.sub.(s) with respect to a position command, and such a characteristic G(s) can be approximated in a software-implemented servo system with a time lag of first order as: ##EQU1## Since a response characteristic V.sub.(t) of the speed with respect to a stepwise speed command (V.sub.0 /S) is given by: EQU V.sub.(t) =V.sub.0 (1-e.sup.P) (2)
where P is -.omega..sub.O t, the acceleration a.sub.(t) required is determined by differentiating the equation ( 2) through first-order differentiation as: EQU a.sub.(t) =V.sub.0 .multidot..omega..sub.0 .multidot.e.sup.P ( 3)
Therefore, assuming that the maximum speed of the mechanical speed is V.sub.O max, the maximum acceleration a.sub.max generated by the positional control system is limited by: EQU a.sub.max =V.sub.O max .multidot..omega..sub.O ( 4)
As the allowable maximum acceleration A.sub.max of the mechanical system is determined by its structure, the maximum acceleration a.sub.max and the allowable maximum acceleration A.sub.max should meet the following relationship: EQU a.sub.max .ltoreq.A.sub.max
Therefore, the maximum value V.sub.0 max of the gain of the position control loop is limited by: EQU .omega..sub.O max =A.sub.max /V.sub.0 max ( 5)
The problem of quick response will be described with reference to an injection molding machine by way of example.
As shown in FIG. 2 of the accompanying drawings, a conventional injection molding machine includes: a mold assembly 6 composed of a fixed mold 2 and a movable mold 4. A metering injection unit 18 is composed of a cylinder 10 having a nozzle 8 on its tip end. A hopper 12 is provided for supplying a synthetic resin material, and a piston 16 disposed in the cylinder 10 and having a metering and supplying screw 14. A metering actuator 26 includes a motor 22 for rotating the piston 16 in the cylinder 10 and a detector 24. An injecting actuator 40 is provided including a motor 30 for moving the piston 16 as well as the metering actuator 26 back and forth with respect to the cylinder 10. A detector 32, a nut member 34, a support 36, and a ball screw 38 are operatively mounted relative to each other. A cylinder actuator 52 includes a motor 42 for moving the cylinder 10 toward and away from the mold 6. A detector 44, a nut member 46, a connecting member 48, and a ball screw 50 are operatively mounted relative to each other. A mold actuator 62 includes a motor 54 for moving the movable mold 4 toward and away from the fixed mold 2. A detector 56, a gear train 58, and a ball screw 60 are operatively mounted relative to each other. A control unit 64 is provided for applying control signals to the actuators 26, 40, 52, and 62; and a position command generator 66. The actuators 26, 40, 52, and 62 and the control unit 64 jointly constitute a control system which is a software-implemented servo system as shown in FIG. 1.
When position commands for the respective actuators 26, 40, 52, and 62 are applied from the position commmand generator 66 to the control unit 64 according to a predetermined program, the mold actuator 62 moves the movable mold 4 toward the fixed mold 2 to form a mold cavity (not shown) for being filled with the synthetic resin material. In addition, the cylinder actuator 52 moves the cylinder 10 to position the nozzle 8 in the injection port (not shown) of the fixed mold 3. The metering actuator 26 is operated in advance to rotate the piston 16 for metering the synthetic resin material supplied from the hopper 12. Further, the injecting actuator 40 is operated to move the piston 16 in the cylinder 10 to inject the synthetic resin material from the cylinder 10 through the nozzle 8 into the mold cavity for thereby molding a desired article within the mold assembly 6.
The quality of the molded article is dependent on the manner in which the synthetic resin material is injected from the metering injection unit 18 into the mold cavity of the mold assembly 6. The manner in which the synthetic resin material is injected is inturn limited by various conditions such as the inner shape of the mold cavity, the kind of the synthetic resin material, the temperature, the design of the metering injection unit 18, and the like. Desired molded products cannot be obtained simply by injecting the synthetic resin material in a single operation. The position control system for the injecting actuator 40 is required to be better in quick response while maintaining stability as compared to a position control system for other actuators. However, such a requirement cannot be met by the above software-implemented servo system.
Since the quick response is thus limited by the mechanical system in the injection molding machine employing the conventional position control system, it has been not possible to control the injecting actuator 40 to carry out the resin injection process under ideal conditions based on a complex position-time diagram (not shown). Further it has been difficult to fabricate high-quality products.
Two-axis control of an X-Y plotter, for example) for drawing a circle will be described in relation to the accuracy problem.
If the accuracy of drawing a circle is expressed by a radius reduction ratio .delta., the radius reduction ratio can be given by: ##EQU2## where R is the radius (mm) of a commanded circle, .DELTA.R is the amount (mm) by which the radius is reduced, and V.sub.0 is the speed (mm/min.).
When drawing a circle having the constant radius R at the constant speed V.sub.0 as indicated by the equation (6), the radius reduction ratio .delta. is proportional to 1/.omega..sub.0.sup.2 (i.e., inversely proportional to .omega..sub.0.sup.2). The maximum gain .omega..sub.0 max of the position control loop is limited in relation to the mechanical system as shown by the equation (5) above. Therefore, since the upper limit of the maximum gain .omega..sub.0 max is determined by the allowable maximum accleration A.sub.max and the maximum speed V.sub.0 max which are determined by the mechanical system in the position control system that is approximated by the equation (1), if the mechanical system (A.sub.max, V.sub.0 max) is fixed, then the upper limit of the maximum gain .omega..sub.0 max is restricted and cannot be increased. As a result, the accuracy (.delta.) is limited by the maximum gain .omega..sub.0 max, and cannot be increased.